The bomber targeted a bus transporting personnel in Sistan-Baluchestan province near the border with Pakistan.
The Sunni Muslim militant group, Jaish al-Adl (Army of Justice), has said it was behind the bombing.
The Revolutionary Guards, set up shortly after the 1979 Islamic Revolution, are a major military, political and economic force in Iran.
What do we know about the attack?
The Revolutionary Guards branch in south-eastern Iran said a unit of its ground forces had been returning from the Pakistan border area on Wednesday when a car filled with explosives blew up beside their bus on the Khash-Zahedan road.
In a statement, it blamed "takfiri terrorists and mercenaries of the intelligence services of hegemonic powers". "Takfiri" is a term used to describe Sunni extremists who see other Muslims as non-believers.
It did not identify the "hegemonic powers", but Iran's foreign minister linked the bombing to a US-led conference on the Middle East taking place in Warsaw, Poland, that will include discussions about Iran's activities in the region.
This is one of the deadliest attacks on the elite forces in years, correspondents say.
Revolutionary Guards take lead on foreign affairs
What do we known about Jaish al-Adl?
Jaish al-Adl took up arms in 2012 to fight for what it says are the rights of Iranian Sunnis, who complain of discrimination by the Shia establishment.
The group has carried out several recent attacks against security personnel in Sistan-Baluchestan, which has a large mainly Sunni ethnic Baluchi community.
Earlier this month, Jaish al-Adl was blamed for an attack on a paramilitary base in Nik Shahr that left one Revolutionary Guard dead and five others wounded.
The group also said it had carried out two bombings that wounded three police officers in Zahedan at the end of January.
And in October, Jaish al-Adl kidnapped at least 10 security personnel, including several Revolutionary Guards, at a border post in Mirjaveh.
In September, gunmen killed at least 24 people at a military parade in the south-western city of Ahvaz.
Both the jihadist group Islamic State (IS) and Iranian ethnic Arab separatists claimed they were behind the assault, but neither provided conclusive evidence.